Article
Full entry |
PDF
(0.3 MB)
Feedback
PDF
(0.3 MB)
Feedback
Keywords:
weak congruence; CEP; WCIP; semimodular lattice; complemented lattice
weak congruence; CEP; WCIP; semimodular lattice; complemented lattice
Summary:
Here we consider the weak congruence lattice $C_{W}(A)$ of an algebra $A$ with the congruence extension property (the CEP for short) and the weak congruence intersection property (briefly the WCIP). In the first section we give necessary and sufficient conditions for the semimodularity of that lattice. In the second part we characterize algebras whose weak congruences form complemented lattices.
References:
[1] P. Crawley and R. P. Dilworth: Algebraic Theory of Lattices. Prentice Hall, Englewood Cliffs, New Jersey, 1973.
[2] E. W. Kiss, L. Marki, P. Pröhle and W. Tholen: Categorical algebraic properties. A compendium on amalgamation, congruence extension, epimorphisms, residual smallness and injectivity. Studia Sci. Math Hung. 18 (1983), 79–141. MR 0759319
[3] B. Šešelja and G. Vojvodič: A note on some lattice characterizations of Hamiltonian groups. Univ. u Novom Sadu, Zb. Rad. Prirod.-Mat. Fak. Ser. Mat. 19 (1989), 179–184. MR 1100270
[4] B. Šešelja and G. Vojvodič: CEP and homomorphic images of algebras. Univ. u Novom Sadu, Zb. Rad. Prirod.-Mat. Fak. Ser. Mat. 19 (1989), 75–80. MR 1099995
[5] B. Šešelja and A. Tepavčevič: Special elements of the lattice and lattice identities. Univ. u Novom Sadu, Zb. Rad. Prirod.-Mat. Fak. Ser. Mat. 20 (1990), 21–29. MR 1158422
[6] B. Šešelja and A. Tepavčevič: Weak congruences and homomorphisms. Univ. u Novom Sadu, Zb. Rad. Prirod.-Mat. Fak. Ser. Mat. 20 (1990), 61–69. MR 1158426
[7] B. Šešelja and A. Tepavčevič: On CEP and semimodularity in the lattice of weak congruences. Univ. u Novom Sadu, Zb. Rad. Prirod.-Mat. Fak. Ser. Mat. 22 (1992), 95–106. MR 1295228
[8] G. Vojvodič and B. Šešelja: Subalgebras and congruences via diagonal relation. In: Algebra and Logic, Proc. of Sarajevo Conf, 1987, pp. 169–177. MR 1102051
[9] G. Vojvodič and B. Šešelja: On the lattice of weak congruence relations. Algebra Universalis 25 (1988), 121–130. DOI 10.1007/BF01229965 | MR 0950740
Search
Partner of
